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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#810654 | #6137. Sub-cycle Graph | wzj33300 | AC ✓ | 282ms | 4740kb | C++23 | 11.7kb | 2024-12-12 08:02:00 | 2024-12-12 08:02:00 |
Judging History
answer
/**
* created : 12.12.2024 00:05:21
* author : wzj33300
*/
#include <bits/stdc++.h>
using namespace std;
#ifdef DEBUG
#include <algo/debug.h>
#else
#define debug(...) 42
#define assert(...) 42
#endif
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using db = long double; // or double, if TL is tight
using str = string; // yay python!
// pairs
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<db, db>;
#define fi first
#define se second
// ^ lol this makes everything look weird but I'll try it
template <class T>
using vc = vector<T>;
template <class T, size_t SZ>
using AR = array<T, SZ>;
using vi = vc<int>;
using vb = vc<bool>;
using vl = vc<ll>;
using vd = vc<db>;
using vs = vc<str>;
using vpi = vc<pi>;
using vpl = vc<pl>;
using vpd = vc<pd>;
// vectors
// oops size(x), rbegin(x), rend(x) need C++17
#define sz(x) int((x).size())
#define bg(x) begin(x)
#define all(x) bg(x), end(x)
#define rall(x) x.rbegin(), x.rend()
#define sor(x) sort(all(x))
#define rsz resize
#define ins insert
#define pb push_back
#define eb emplace_back
#define ft front()
#define bk back()
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rep1(i, n) for (int i = 1; i < (n); ++i)
#define rep1n(i, n) for (int i = 1; i <= (n); ++i)
#define repr(i, n) for (int i = (n) - 1; i >= 0; --i)
#define rep_subset(t, s) \
for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define lb lower_bound
#define ub upper_bound
template <class T>
int lwb(vc<T>& a, const T& b) {
return int(lb(all(a), b) - bg(a));
}
template <class T>
int upb(vc<T>& a, const T& b) {
return int(ub(all(a), b) - bg(a));
}
// const int MOD = 998244353; // 1e9+7;
const int Big = 1e9; // not too close to INT_MAX
const ll BIG = 1e18; // not too close to LLONG_MAX
const db PI = acos((db)-1);
const int dx[4]{1, 0, -1, 0}, dy[4]{0, 1, 0, -1}; // for every grid problem!!
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
int pct(int x) { return __builtin_popcount(x); }
int pct(u32 x) { return __builtin_popcount(x); }
int pct(ll x) { return __builtin_popcountll(x); }
int pct(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
T floor(T a, T b) {
return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
T q = floor(x, y);
return {q, x - q * y};
}
template <class T>
bool ckmin(T& a, const T& b) {
return b < a ? a = b, 1 : 0;
} // set a = min(a,b)
template <class T>
bool ckmax(T& a, const T& b) {
return a < b ? a = b, 1 : 0;
} // set a = max(a,b)
template <class T, class U>
T fstTrue(T lo, T hi, U f) {
++hi;
assert(lo <= hi); // assuming f is increasing
while (lo < hi) { // find first index such that f is true
T mid = lo + (hi - lo) / 2;
f(mid) ? hi = mid : lo = mid + 1;
}
return lo;
}
template <class T, class U>
T lstTrue(T lo, T hi, U f) {
--lo;
assert(lo <= hi); // assuming f is decreasing
while (lo < hi) { // find first index such that f is true
T mid = lo + (hi - lo + 1) / 2;
f(mid) ? lo = mid : hi = mid - 1;
}
return lo;
}
template <typename T>
T inverse(T a, T m) {
T u = 0, v = 1;
while (a != 0) {
T t = m / a;
m -= t * a;
swap(a, m);
u -= t * v;
swap(u, v);
}
assert(m == 1);
return u;
}
template <typename T>
class Modular {
public:
using Type = typename decay<decltype(T::value)>::type;
constexpr Modular() : value() {}
template <typename U>
Modular(const U& x) {
value = normalize(x);
}
template <typename U>
static Type normalize(const U& x) {
Type v;
if (-mod() <= x && x < mod())
v = static_cast<Type>(x);
else
v = static_cast<Type>(x % mod());
if (v < 0) v += mod();
return v;
}
const Type& operator()() const { return value; }
template <typename U>
explicit operator U() const { return static_cast<U>(value); }
constexpr static Type mod() { return T::value; }
Modular& operator+=(const Modular& other) {
if ((value += other.value) >= mod()) value -= mod();
return *this;
}
Modular& operator-=(const Modular& other) {
if ((value -= other.value) < 0) value += mod();
return *this;
}
template <typename U>
Modular& operator+=(const U& other) { return *this += Modular(other); }
template <typename U>
Modular& operator-=(const U& other) { return *this -= Modular(other); }
Modular& operator++() { return *this += 1; }
Modular& operator--() { return *this -= 1; }
Modular operator++(int) {
Modular result(*this);
*this += 1;
return result;
}
Modular operator--(int) {
Modular result(*this);
*this -= 1;
return result;
}
Modular operator-() const { return Modular(-value); }
template <typename U = T>
typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
return *this;
}
template <typename U = T>
typename enable_if<is_same<typename Modular<U>::Type, long long>::value, Modular>::type& operator*=(const Modular& rhs) {
long long q = static_cast<long long>(static_cast<long double>(value) * rhs.value / mod());
value = normalize(value * rhs.value - q * mod());
return *this;
}
template <typename U = T>
typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type& operator*=(const Modular& rhs) {
value = normalize(value * rhs.value);
return *this;
}
Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }
friend const Type& abs(const Modular& x) { return x.value; }
template <typename U>
friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);
template <typename U>
friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);
template <typename V, typename U>
friend V& operator>>(V& stream, Modular<U>& number);
private:
Type value;
};
template <typename T>
bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value == rhs.value; }
template <typename T, typename U>
bool operator==(const Modular<T>& lhs, U rhs) { return lhs == Modular<T>(rhs); }
template <typename T, typename U>
bool operator==(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) == rhs; }
template <typename T>
bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T, typename U>
bool operator!=(const Modular<T>& lhs, U rhs) { return !(lhs == rhs); }
template <typename T, typename U>
bool operator!=(U lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T>
bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value < rhs.value; }
template <typename T>
Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U>
Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U>
Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T>
Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U>
Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U>
Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T>
Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U>
Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U>
Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T>
Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U>
Modular<T> operator/(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U>
Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
assert(b >= 0);
Modular<T> x = a, res = 1;
U p = b;
while (p > 0) {
if (p & 1) res *= x;
x *= x;
p >>= 1;
}
return res;
}
template <typename T>
bool IsZero(const Modular<T>& number) {
return number() == 0;
}
template <typename T>
string to_string(const Modular<T>& number) {
return to_string(number());
}
// U == std::ostream? but done this way because of fastoutput
template <typename U, typename T>
U& operator<<(U& stream, const Modular<T>& number) {
return stream << number();
}
// U == std::istream? but done this way because of fastinput
template <typename U, typename T>
U& operator>>(U& stream, Modular<T>& number) {
typename common_type<typename Modular<T>::Type, long long>::type x;
stream >> x;
number.value = Modular<T>::normalize(x);
return stream;
}
// using ModType = int;
// struct VarMod { static ModType value; };
// ModType VarMod::value;
// ModType& md = VarMod::value;
// using Mint = Modular<VarMod>;
constexpr int md = 1e9 + 7;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
vector<Mint> fact(1, 1);
vector<Mint> inv_fact(1, 1);
Mint C(int n, int k) {
if (k < 0 || k > n) {
return 0;
}
while ((int)fact.size() < n + 1) {
fact.push_back(fact.back() * (int)fact.size());
inv_fact.push_back(1 / fact.back());
}
return fact[n] * inv_fact[k] * inv_fact[n - k];
}
Mint p2[100005];
void _sol() {
ll n, m;
cin >> n >> m;
C(n, 0);
if (m > n)
cout << 0 << endl;
else if (m == n)
cout << fact[n] / 2 / n << endl;
else if (m == 0)
cout << 1 << endl;
else {
Mint ans = 0;
for (int one = 0; one < n - m; one++) {
int remain = n - m - one;
Mint now = 1;
now = C(m - 1, remain - 1) * C(n, one) * fact[n - one] * p2[remain] * inv_fact[remain];
ans += now;
}
cout << ans << '\n';
}
}
// signed main() {
int main() {
// freopen(".in", "r", stdin);
// freopen(".out", "w", stdout);
ios::sync_with_stdio(false);
cin.tie(0);
p2[0] = 1;
for (int i = 1; i <= 100000; i++) p2[i] = p2[i - 1] / 2;
int t;
cin >> t;
while (t--) {
_sol();
}
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 1ms
memory: 4212kb
input:
3 4 2 4 3 5 3
output:
15 12 90
result:
ok 3 number(s): "15 12 90"
Test #2:
score: 0
Accepted
time: 282ms
memory: 4740kb
input:
17446 3 0 3 1 3 2 3 3 4 0 4 1 4 2 4 3 4 4 5 0 5 1 5 2 5 3 5 4 5 5 6 0 6 1 6 2 6 3 6 4 6 5 6 6 7 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 8 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 9 0 9 1 9 2 9 3 9 4 9 5 9 6 9 7 9 8 9 9 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 11 0 11 1 11 2 11 3 11 4 11 5 11 6 11 7 11...
output:
1 3 3 1 1 6 15 12 3 1 10 45 90 60 12 1 15 105 375 630 360 60 1 21 210 1155 3465 5040 2520 360 1 28 378 2940 13545 35280 45360 20160 2520 1 36 630 6552 42525 170100 393120 453600 181440 20160 1 45 990 13230 114345 643545 2286900 4762800 4989600 1814400 181440 1 55 1485 24750 273735 2047815 10239075 3...
result:
ok 17446 numbers